A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysi...A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.展开更多
China is one of the countries in the world carrying a heavy burden of tuberculosis.Due to the unbalanced economic development,the number of people working in other parts of country is huge,and the mobility of personne...China is one of the countries in the world carrying a heavy burden of tuberculosis.Due to the unbalanced economic development,the number of people working in other parts of country is huge,and the mobility of personnel has exacerbated the increase in tuberculosis cases.Most patients affected by this are in their middle and young ages.It is having a great impact among the family and society.Therefore,research on how to control this disease is absolutely necessary.The population is divided into two categories such as local population and the immigrant population.A pulmonary tuberculosis dynamic model with population heterogeneity is established.We calculate the basic reproductive number and the controlled reproductive number,and discuss the two types of population under the constraints given by the amount of vaccine and the optimal immunization ratio obtained is(0.118,0.107),which can reduce the effective reproduction number from 5.85 to 0.227.It is understood that immunizing the local population will control the spread of the epidemic to a large extent,and we simulate the final scale of infection after immunization under the optimal immunization ratio.It can take a minimum of at least 10 years to reduce the spread of this disease,but to eliminate it forever,it needs at least a minimum of 100 years.展开更多
基金Supported by Research Council of Semnan University
文摘A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.
基金This study was funded by the Natural Science Foundation of China(NSFC 11871093 and 11901027)Postgraduate Teaching Research and Quality Improvement Project of BUCEA(J2021010)BUCEA Post Graduate Innovation Project(PG2022139)。
文摘China is one of the countries in the world carrying a heavy burden of tuberculosis.Due to the unbalanced economic development,the number of people working in other parts of country is huge,and the mobility of personnel has exacerbated the increase in tuberculosis cases.Most patients affected by this are in their middle and young ages.It is having a great impact among the family and society.Therefore,research on how to control this disease is absolutely necessary.The population is divided into two categories such as local population and the immigrant population.A pulmonary tuberculosis dynamic model with population heterogeneity is established.We calculate the basic reproductive number and the controlled reproductive number,and discuss the two types of population under the constraints given by the amount of vaccine and the optimal immunization ratio obtained is(0.118,0.107),which can reduce the effective reproduction number from 5.85 to 0.227.It is understood that immunizing the local population will control the spread of the epidemic to a large extent,and we simulate the final scale of infection after immunization under the optimal immunization ratio.It can take a minimum of at least 10 years to reduce the spread of this disease,but to eliminate it forever,it needs at least a minimum of 100 years.
